Representing an isotone map between two bounded ordered sets by principal lattice congruences
For bounded lattices L1 and L2, let (Formula presented.) be a lattice homomorphism. Then the map (Formula presented.), defined by (Formula presented.), is a 0-preserving isotone map from the bounded ordered set Princ(L1) of principal congruences of L1 to that of L2. We prove that every 0-preserving...
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| Format: | Article |
| Published: |
2018
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| Series: | ACTA MATHEMATICA HUNGARICA
155 No. 2 |
| doi: | 10.1007/s10474-018-0844-5 |
| mtmt: | 3394288 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/14540 |
| Summary: | For bounded lattices L1 and L2, let (Formula presented.) be a lattice homomorphism. Then the map (Formula presented.), defined by (Formula presented.), is a 0-preserving isotone map from the bounded ordered set Princ(L1) of principal congruences of L1 to that of L2. We prove that every 0-preserving isotone map between two bounded ordered sets can be represented in this way. Our result generalizes a 2016 result of G. Grätzer from (Formula presented.)-preserving isotone maps to 0-preserving isotone maps. © 2018 Akadémiai Kiadó, Budapest, Hungary |
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| Physical Description: | 332-354 |
| ISSN: | 0236-5294 |